As a method of preparing base stocks for lubricating oil, it has been known to refine an intermediate product by comparatively mild hydrogenation, so-called hydrofinishing. However, base stocks for lubricating oil with excellent thermal stability can not be obtained by this process. Thus in order to overcome the above defect, as a modified process it has been proposed that hydrofinishing is carried out after extraction of an intermediate product with such a solvent as furfural, phenol, etc., as described in Oil and Gas Journal, Vol. 53, No. 26, p.81-84 (1954). However, according to this process, 20-30 percent of charge stocks are removed as the extract by solvent extraction and thus the product yield is decreased. On the other hand, it has been proposed to obtain base stocks for lubricating oil with excellent thermal stability by only an extraction process. However, according to this process, it is essential to remove undesirable components extensively for thermal stability and thus substantial amounts of desirable materials are moved to the extract. Therefore, further reduction of the raffinate yield, i.e. the product yield, can not be avoided. These extracts are used as a heavy oil and useful components as a lubricating oil are not used effectively.